The present invention relates to a living body internal active source estimation apparatus for estimating positions and moments of active sources in a living body on the basis of electromagnetic field distribution observed on the living body surface.
Heretofore, when estimating active sources in a living body on the basis of electromagnetic distribution observed on the living body surface, current dipoles were used in substitution for main active sources in the brain, and the positions and the moments of the dipoles were estimated. The estimation of the positions and the moments of the dipoles from the observed electromagnetic field distribution, was executed by, for instance, a method as described in the following.
An electromagnetic model of a living body is used, and it is assumed that dipoles are generated in the living body. With these dipoles, an electromagnetic field distribution, which would be recorded at an observation point placed on a surface, is calculated.
Then, denoting the calculated value of the electromagnetic field distribution at i-th observation point by .o slashed..sub.i.sup.(dip) and an observed value obtained by actual measurement by .o slashed..sub.i.sup.(mes), the sum of squares of the residuals r, for instance, is calculated as a residual function of these values expressed as: ##EQU1##
If the sum of squares of the residuals r is greater than a predetermined value, the positions and moments of the dipoles are corrected by using an optimization method based on numerical analysis, typically a Marquardt method or a Simplex Method, for reducing the sum of squares of the residuals r.
When dipole positions and moments are obtained such that they reduce the sum of squares of the residuals r to be less than the predetermined value, they are executed to be a result of estimation.
The above method is described in detail in Bin He et al., "Electric Dipole Tracing in the Brain by Means of the Boundary Element Method and Its Accuracy", IEEE dTransactions on Biomedical Engineering, Vol., BME-34., No. 6, June 1978 (hereinafter referred to as Literature 1).
An estimation method based on a regional dipole source model, is carried out by assuming a relatively large number of dipoles in a living body and fixing the positions and moments of these dipoles for estimating only the size of these dipoles.
In this method, denoting the dipole size to be estimated by q.sub.j, by using a matrix F which is calculated from an electromagnetic model of the living body and the positions and directions of the dipoles, the observed value .o slashed..sub.i.sup.(mes) is expressed as: ##EQU2##
Usually, the number of dipoles is greater than that of observed data. Thus, it is possible to estimate dipole size qi by obtaining the generalized inverse matrix F+ of the matrix F. This estimated dipole size is given as: EQU q=F.sup.+.o slashed..sup.(mes). (3)
The above method is detailed in J. Z. Wang et al., "Magnetic Source Image Determined by a Lead-Field Analysis: The Unique Minimum-Norm Least-Squares Estimation", IEEE Transactions on Biomedical Engineering, Vol. BME-39, No. 7, July 1992 (hereinafter referred to as Literature 2).
The above prior art techniques, however, have the following problems.
(1) In the above method for estimating the positions and the moments of dipoles, it is necessary to repeatedly carry out the calculation a large number of times. Therefore, extremely long time should be spent until obtaining the final positions and moments of dipoles. In addition, increase of the number of assumed dipoles leads to enormous time required for the estimation. Besides, since an activity at a certain point is assumed to be a dipole, it is impossible to obtain optimal solutions for an active source having certain region.
(2) In the method using a regional dipole source model, if the observed data contains even slight noise, the data corresponding to the noise is greatly reflected on the estimation result, resulting in deterioration or loss of reliability.